Maximum power transfer theorem and Reciprocity theory

Prerequisites



Other basics: [ CROInductor, Capacitor ]

Experiment for Maximum power transfer theorem

$Z_i = R_i + X_i = constant$

Maximum power will be delivered, when current through the load is maximum.

Adjust $X_L$ so that maximum power is transferred

Condition: $X_L = -X_i$
$ \qquad \Rightarrow |X_L|= |X_i|$
$ \qquad \Rightarrow \frac{1}{wC} = wL$
$ \qquad \Rightarrow C = \frac{1}{w^2 L}$

Vary $C$ so that it will satisfy the above condition; and at that point, we will have $V_1 V_3$ value maximum and $V_2 = V_4$.

Adjust $R_L$ so that maximum power is transferred

If capacitor is constant, assume it as a part of source impedance. Now, vary $R_L$ so that it will come closer to the source impedance.
Then, $R_L = \sqrt {R_i^2 + (X_i + X_L)^2}$

Adjust both $X_L$ and $R_L$ so that maximum power is transferred
Conditions:

$ |X_L|= |X_i| \qquad \Rightarrow V_4 = V_2$
$ |R_L|= |R_i| \qquad \Rightarrow V_3 = V_1$



Experiment for Reciprocity theory



-Connect the components as per circuit diagram.
- Provide supply to port 1 ($V_1$) and measure current through port 2 ($I'$).
- Change the power supply and ammeter position. i.e. Provide supply to port 2 ($V_2$) and measure current through port 1($I''$).
- Check that, $ \frac{V_1}{I'} = \frac{V_2}{I''}$